What are the most common beginner mistakes when learning Blender?
Double Vertices - Most often caused by extruding something, cancelling the move afterwards, and then extruding again. Can be fixed by selecting all by pressing A, then pressing Ctrl + V, and choosing 'Remove Doubles'.
Flipped Normals - This can have many causes. It's visible as odd shading on a model, but is often a bit hard to pick out. Can be fixed by selecting all, then pressing Ctrl + N.
Unapplied Rotation and Scale - If the scale of an object is not 1 or its rotation is not 0 degrees on all axes, a lot of actions can have strange results. Unless there is a specific reason not to apply rotation or scale, can be fixed by pressing Ctrl + A and selecting the appropriate option.
Hidden things - Pressing H makes whatever is selected invisible. Pressing Alt + H unhides things. 
Unnessesary Ngons - Faces with more than 4 connected vertices (Ngons) may cause shading issues, and should be minimized. Ctrl + T triangulates the mesh, and can help avoid these problems.